Question

1. You have been asked to find the volume of a small pond. Assume that the pond is perfectly mixed and that there is no flow into or out of the pond. you dump 5L of a 3M solution of a dye which degrades with a half life of 5 days. you take a 100ml sample after 1 week. the dye's concentration in the sample is 1 x 10^-6 M. what is the pond volume.

Answer 1

Suppose the volume of the pond is V Litre

Initial concentration of dye in pond (M1) = (Initial concentration of solution x Initial volume)/ volume of pond

                                                                          = 3 x 5/V = 15/V Litre

K = 0.6932/t_1/2

K = 0.6932/5 = 0.13864

K = 2.303/t log M_i/M_f

0.13864 = 2.303/7 log 15/(V x 10^-6)

0.4214 = log 15000000/V

log 2.6388 = log 15000000/V

2.6388 = 15000000/V

V = 5684402 Litre